Sheet metal building construction



' D88. 11, 1934. A WISE 1,983,828

SHEET METAL BUILDING CONSTRUCTION Filed Oct. 15, 19s0 SSheets-Sheet 2 gz /v I: Ol9

gwuemkov Jose ti )2- Wise Dec. 11, 1934. 55

SHEET METAL BUILDING CONSTRUCTION 3 Sheets-Shet 5 Filed Oct. 15, 1930 gwumdoo Jose 9127 Wise Patented Dec. 11, 1934 UNITED STATES PATENT OFFICE Application October 15,

10 structure wherein the sheet metal wall and roof covering constitutes the primary load carrying system which is rendered amply strong by a continuous arch form of roof and deep corrugations.

Another object is to providesheet metal con- 15 struction permitting ready fastening of the several component parts or units together and also adapted to give a maximum of salvage when the building is torn down.

To facilitate computations of the depths of 20 corrugations for various spans to meet specifica- ..tiq ns for roofs of varying load capacity, I have also devised a mathematical formula for calcu- 1 Plating the buckling load on my arched and corrugated roof.

The invention may be applied to buildings of any length, but itis most economically used for widths or spans of arch up to about fifty feet because of practical limitations on the depth of corrugations and thickness of sheets required for the larger spans.

The invention, will be best understood by reference to the accompanying drawings in which Figures 1 and 2 are side and end views of a building constructed in accordance with my invention; Fig. 3 is a plan view of the building with the roof removed; Fig. 4 is a fragmentary, vertical section taken on the line 4-4 of Fig. 5 and showing the stops for the corrugations beneath the eaves of the building; Fig. 5 is a fragmentary, vertical section through one of the side walls and adjacent portion of the roof; Fig. 6 is a fragmentary, vertical section taken on the line 6-6 of Fig. 3 with a portion of the roof added; Fig. '7 is an enlarged plan view showing the; corner connections between the sideand end walls and a fragmentary portion of the roof; Fig.- 8 is a section taken on the line 8-8 of Fig. 6; Fig. 9 is a transverse section through the building taken on the line 9.--9 of Fig. 1; Fig. 10 is a diagrammatic illustration of the form of corrugation with suitable dimensions for the larger spans indicated thereon; Fig. 11 Tea diagram explanatory of the mathematical formula for calculating the buckling loads for mycon ugate'd, arch roof, and Fig. 12 is a diagrammatic explanation of the 1930, Serial No. 488,761

symbols employed in the derivation of the general differential equation for curved beams.

My improved building has end walls 13, side walls 14 and a roof 15 all-constructed from sheet steel or other suitable metal formed with deep 5 corrugations. The roof is of continuous arch form with the corrugations extending circumferentially'and is supported entirely on the side and end walls, no trusses or supporting columns being provided. Each corrugation is preferably 10 formed with a flat inner and outer surface to facilitate connecting the several units or panels together. Both the walls and roof are preferably formed in long panels extending longitudinally of the corrugations and of a width equal to three 15 orfour of the corrugations. For the joint with the side walls, a continuous plate 16 is welded to the roof sheet and is formed with a pendant flange 17 to be bolted to the wall sheets (see Fig. 5). Each panel of the side walls 14 has secured to the outer surfaces of its corrugations a strip 18 of light gauge metal and bolts 19 for securing the side walls to the roof are passed through perforations in the flange 17, strip 18, side walls and also in stop plates 20 which, as best shown in Fig. 4, close the roof corrugations. An angle bar 21 extends longitudinally of the roofnear the eaves and is secured by bolts 22 to the roof sheet and to the plate 16.

Tie rods 23 join the angle bars 21 at opposite sides of the roof together; these tie rods being provided to sustain the horizontal component of the end thrust delivered by the arched roof. At suitable intervals struts 24 connect the angle bars 21 together and angle clips 25 are employed to make the connections between the bars 21 and ends of the struts 24. Diagonal brace rods 26 are connected to the ends of the struts 24 and, at the ends of the building, these rods 26 are secured to angle clips on the bars 21. Horizontal beams 27 are joined to the angle bars 21 by angle clips 28 adjacent to the end walls 13 (Figs. 7

and 8).

Ateach vertical corner of the building an angle bar 29 is connected to the horizontal beams 27 by triangular plates 30 and at-their lower ends the angle bars 29 are'connected in pairs by triangular plates secured to channel beams 31. Suitable diagonals 32 are also joined to the corner bars 29, as best shown in Fig. 2. At the base of each side wall, an angle bar 33 is secured to the inner surfaces of the corrugations.

The corner angle bars 29 are of light weight, designed merely'to make connection between the sideand end walls. Thus it will be evident that feet in width and where sheet steel of from about 16 to 24-gauge is employed. The corrugated sheets commonly employed for wall and roof covering are wholly inadequate to sustain the primary loads for structures of the size contemplated herein. As far as I am aware, corrugated steel with a maximum-depth of corrugations of about three-fourths of an inch is the stiilest that has heretofore been employed for roof or wall covering. The moment of inertia of corrugated steel ofsuch common,weight and depth of corrugation is approximately .05 inch to the fourth.

power per foot width of sheet, whereas, a building having an arched roof with a span as small as sixteen feet requires corrugations and weight of. material such as to give a moment of inertia of approximately .07 inch to the fourth power per foot width of sheet.

My mathematical formula for calculating the buckling loads for arched, corrugated roofs is derived from the general differential equation for curved beams, and will be understood by a reference to Fig. 11, in which a circular curve representing a suitable form of arch is indicated by the numeral 34. For fairly flat arches, the snow load on a roof can be fairly represented by a uniformly distributed load w per unit of length of horizontal projection of arch. The general differential equation for curved beams, first derived by Boussineso, is obtained by the following derivation. From Fig. 12:

rdO d+Ad0 1 l L I; we: From the common theory of fiexure:

zAcl6 I we f=unit fiber stress, M=bending moment. I=moment of inertia. e=unit strain. Modulus of elasticity, E is defined as:

Mrd6 e IAd0 or LL! V raid El therefore, substituting in (1) Let the radius vector of any point on the deformed curve be R=r+y. (See Fig. 11.) The radius of curvature expressed in terms of R and its derivatives is:

tute (r+y) for R and omit all quantities that are very small compared to the terms to they are added, as

etc. we get, noting that p. 7J5? Substituting (4) in 2) we get:

which M EI or d v M 3+y= 279 2 1V) 2 r3; is small compared to 1 hence:

d v Mr +Y= This is the basic differential equation of fiexure for curved beams.

Now in order to determine the buckling load, let us first assume a constant compressive stress N throughout the beam. The moment it produces The general solution of Equation (6) is then:

21:00 sin [90+C'1 00$ 50 .(7) From boundary conditions y=0 when 0=ia we find Co=C1=0. that is, no deflection occurs. However, a particular solution of (6).

y=Csin n -(8) will satisfy the end conditions. In this equation the coefiicient C can be any value and its indeterminateness indicates that this is the equation of the elastic line at buckling, for y can then increase indefinitely without any change in N. n is any integer and we choose the smallest possible value to get the minimum buckling load. If n=1, the curve lies entirely on one side of the original curve, which implies a change in length of arc. Since the arc cannot change appreciably, n=1 is barred and we use n=2 as the value giving the lowest mode of buckling. The curve is shown dotted in Fig. 11. It has a node at the vertex. In order that Equation (7) may satisfy Equa- 7| 3 I l I N2 Equation. (9) gives the critical or buckling load.

Solving for N,

M mds 2Ir sin a -The character m in this equation is the'moment tie rods.

1 sin a cos a-I-bz cos aa 11- 6 2 z (10) z 3 a a 21mm ar-asln a-z sin 2a+ A12 The average compression in the arch, isi

a 2 f d H sin a+wr(% Applying these formulae to the design of roofs, the procedure is:

(1) CalculateH from (10) assuming an approximate value for assumed in .(i). If error islarge, recalculate.

To illustratethe use of these formulae, the following example 'will be'taken. Arch roof,. span 30'0", rise 5'-0", w=45 lbs. per sq. ft.

r=2 5".O" a=tan- %=a6'52'=.e435 rad.

By Formula (10), H=1037 lbs. assuming By Formula (11) Navg.=1144 lbs. By Formula (9) I:e .=.1505 inches to the fourth power.

Introducing a factor of safety of 3, 1:.4515 would be used.

Having described my invention what I claim as new and desire to protect by Letters Patent is: .1. A building having a sheet metal, continuous arched roof covering formed with deep corrugations extending circumferentially, sheet metal wall covering having deep corrugations extending vertically, tie rods for sustaining the horizontal component of end thrust, said tie rods being connected to the roof covering near the junctionof the same with said wall covering, the span of the arch between walls being in excess of fifteen feet and said wall and roof covering constituting the principal load supporting system and the several corrugations of the roof transmitting equal loads to the supporting walls.

2. A sheet metal building having a sheet metal, continuous arched covering formed with deep corrugations extending circumferentially, sheet metal wall covering having deep corrugations extending vertically, tie rods for sustaining the horizontal component of end thrust, said tie rods extending substantially horizontally and being connected to the roof covering near the junction of the same with said wall covering the span of the arch between walls being in excess of fifteen feet and not more than fifty feet and said wall and roof covering constituting the primary load supporting system without columns or trusses.

JOSEPH A. WISE. 

